## Compounds

So far, we have only discussed moles, mass and molar mass in relation to *elements*. But what happens if we are dealing with a compound? Do the same concepts and rules apply? The answer is *yes*. However, you need to remember that all your calculations will apply to the *whole compound*. So, when you calculate the **molar mass** of a covalent compound, you will need to add the molar mass of each atom in that compound. The number of moles will also apply to the whole molecule. For example, if you have one mole of nitric acid (\(\text{HNO}_{3}\)) the molar mass is \(\text{63.01}\) \(\text{g·mol$^{-1}$}\) and there are \(\text{6.022} \times \text{10}^{\text{23}}\) molecules of nitric acid. For network structures we have to use the **formula mass**. This is the mass of all the atoms in **one formula unit** of the compound. For example, one mole of sodium chloride (\(\text{NaCl}\)) has a formula mass of \(\text{63.01}\) \(\text{g·mol$^{-1}$}\) and there are \(\text{6.022} \times \text{10}^{\text{23}}\) molecules of sodium chloride in one formula unit.

In a balanced chemical equation, the number that is written in front of the element or compound, shows the **mole ratio** in which the reactants combine to form a product. If there are no numbers in front of the element symbol, this means the number is ‘1’.

### Optional Video: The Mole and Avogadro’s Number

E.g. \(\text{N}_{2} + 3\text{H}_{2} \rightarrow 2\text{NH}_{3}\)

In this reaction, 1 mole of nitrogen molecules reacts with 3 moles of hydrogen molecules to produce 2 moles of ammonia molecules.

## Example: Calculating Molar Mass

### Question

Calculate the molar mass of \(\text{H}_{2}\text{SO}_{4}\).

### Step 1: Give the molar mass for each element

Hydrogen = \(\text{1.01}\) \(\text{g·mol$^{-1}$}\)

Sulphur = \(\text{32.1}\) \(\text{g·mol$^{-1}$}\)

Oxygen = \(\text{16.0}\) \(\text{g·mol$^{-1}$}\)

### Step 2: Work out the molar mass of the compound

\begin{align*} M_{\text{H}_{2}\text{SO}_{4}} = 2(\text{1.01}\text{ g·mol$^{-1}$}) + (\text{32.1}\text{ g·mol$^{-1}$}) + 4(\text{16.0}\text{ g·mol$^{-1}$}) \\ & = \text{98.12}\text{ g·mol$^{-1}$} \end{align*}

## Example:

### Question

Calculate the number of moles in \(\text{1}\) \(\text{kg}\) of \(\text{MgCl}_{2}\).

### Step 1: Convert mass into grams

\[m = \text{1}\text{ kg} \times \frac{\text{1 000}\text{ g}}{\text{1}\text{ kg}} = \text{1 000}\text{ g}\]

### Step 2: Calculate the molar mass

\[M_{\text{MgCl}_{2}} = \text{24.3}\text{ g·mol$^{-1}$} + 2(\text{35.45}\text{ g·mol$^{-1}$}) = \text{95.2}\text{ g·mol$^{-1}$}\]

### Step 3: Find the number of moles

\begin{align*} n & = \frac{\text{1 000}\text{ g}}{\text{95.2}\text{ g·mol$^{-1}$}} \\ & = \text{10.5}\text{ mol} \end{align*}

There are \(\text{10.5}\) \(\text{moles}\) of magnesium chloride in a \(\text{1}\) \(\text{kg}\) sample.

## Optional Discussion: Understanding moles, molecules and Avogadro’s number

Divide into groups of three and spend about 20 minutes answering the following questions together:

What are the units of the mole? Hint: Check the definition of the mole.

You have a \(\text{46}\) \(\text{g}\) sample of nitrogen dioxide (\(\text{NO}_{2}\))

How many

**moles**of \(\text{NO}_{2}\) are there in the sample?How many moles of nitrogen atoms are there in the sample?

How many moles of oxygen atoms are there in the sample?

How many

**molecules**of \(\text{NO}_{2}\) are there in the sample?What is the difference between a mole and a molecule?

The exact size of

**Avogadro’s number**is sometimes difficult to imagine.Write down Avogadro’s number without using scientific notation.

How long would it take to count to Avogadro’s number? You can assume that you can count two numbers in each second.